Asymptotic theory of guided modes in two parallel, identical dielectric waveguides

The guided modes supported by two parallel, identical planar dielectric waveguides are investigated exactly by a quasi-optical technique and approximately by using the improved coupled-mode theory. The wave numbers obtained by the two methods are expanded into asymptotic series in terms of a suitable small parameter. By comparing the asymptotic series obtained by the two methods term by term, it is shown that the improved coupled-mode theory is asymptotically exact in the limit of weak coupling and not so in the strong-coupling regime. The merits and the defects of the improved coupled-mode theory are discussed.